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Distance from (x, y) to (a, b) equals r.
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For x² + y² = r² ⇒ centre (0,0). For (x − a)² + (y − b)² = r² ⇒ centre (a, b).
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(x − 5)² + (y + 4)² = 3² ⇒ (x − 5)² + (y + 4)² = 9.
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Radius = half of AB; centre = midpoint of A and B.
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Group x & y, complete squares, compare with (x − a)² + (y − b)² = r².
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Facts: angle in semicircle = 90°, radius ⟂ tangent, perpendicular from centre bisects a chord.
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Centre at intersection of two perpendicular bisectors.
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Use AB vs r₁, r₂: AB>r₁+r₂ (separate), AB=r₁+r₂ (external touch), AB<|r₁−r₂| (one inside), etc.
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Common chord joins intersection points; length via Pythagoras.
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Substitute line into circle ⇒ quadratic; two solutions = 2 intersections.
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After substitution, discriminant = 0 (repeated root) ⇒ tangent.
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Centres on x-axis; compare centre distance with |r₁−r₂| to show smaller is inside.